Friday, February 17, 2012

Math/Schmath

Albert Pujols and Prince Fielder fled the National League for the DH-friendlier confines of the American League. There is panic in the world of National League-only fantasy baseball players over the dearth of first baseman capable of earning double digits this year. Over at Patton & Co. the panic is evident: “Pujols/Fielder emigration leaves Votto all alone at the top. He's already been an MVP. Looks like Joey's the Man. Raise the prices,” followed by: “Math-Schmath, it's the counting numbers that make Votto so valuable. They're in the hundreds, so compared to, say, ANYONE else in the NL, he's quite a bit better across the board. In keeper leagues, any leg up is a big advantage. And he did hit 37 homers in 2010 and still resides in that tiny park.”

So here is the question: do we jack up the price of Joey Votto in order to account for the loss of Pujols/Fielder? You may not believe me, but the answer is a resounding yes…read on to see by how much.

Now Mike did a fabulous job of explaining position scarcity in deep league auctions. The great lesson from this post is “value trumps scarcity.” Not a scientific law, of course, but true enough of the time that we need to pay attention to it. It would also be instructive to look at his earlier post on position scarcity generally. Mike and I agree on the position scarcity model, so certainly keep that in mind as you read on to the rest of the post.

It is true first base this year is not what it was last year. The loss of Fielder and Pujols is a significant one. In fact, $67 of value (based on last year’s formulas) goes out of the auction, and out of first base, with those two men alone. What does it mean, however, for this year’s pool? Well, AskRotoman already did the math for me, so I will borrow his work and thank him in advance. If you have $75 in bids for Pujols/Fielder, the money must be spent somewhere (the zero-sum game of the auction, fodder for another piece later). Assuming the incoming players are replacement level players, then the overall prices of everyone in the pool would rise by 2.2%. That’s right: 2.2%, or $.79. A $1.00 raise for Joey Votto.

Ah, but, wait - we are still not done the analysis. The players replacing Pujols/Fielder are likely not mere replacement level players (well, Mat Gamel owners will have to pray a novena); they will be getting full time at-bats, and they will be worth more than $1. Using just replacement first basemen as an example, Mike Cuddyer is now in the league and now qualifying at first base…he put up a 3.2 oWAR last year. So, the $.79 raise is, in actuality, even less.

Now that I stretched my poor math skills beyond my level of comfort, let me return to prose for a moment, because I agree with the Patton poster: math/schmath. This is a common sense proposition, explained with words as easily as with math. Joey Votto deserves a raise, but that raise is really $1-$2 at most. The fact that he is that significantly better at his position than the next guy down does not warrant a significant overpay for him. In fact, if you league begins to push Votto well beyond his price point, you should smile to yourself and be prepared to pounce. Why? The bargains will come…the bargains MUST come.

For a moment, let us assume that Joey Votto has a raw bid of $36. Let us also assume you play in an NL-only league with 20% inflation. Now, Joey Votto is priced at $43. By all means, pay $43 for Joey Votto if your roster dictates. In fact, you could/should pay Votto $44 or $45 to account for the first base drop off, the percentage increase in value of all player salaries (essentially applying inflation in a non-linear way), and his slight increase in relative value of stats.

Here is the catch…let us now assume Joey Votto goes for $53, or $10 over inflation par. Well, in the finite universe known as “the auction,” $10 over inflation par equals $10 that cannot be spent on other players, which means $10 in bargains. Now, that $10 will more likely than not be applied in a more linear manner – you will not see Michael Morse or Freddie Freeman suddenly drop in for $14. But let me use a couple of extreme examples to illustrate my point (and I am fudging a bit on the numbers since my actual bids are not finalized yet).

What if Troy Tulowitzki drops in for $33 instead of an inflation-par $37? And Lee falls in for a par $28 instead of inflation-par $33/$34? You may have paid $53 to lock in Joey Votto’s first base-best $33 stats, but you now allowed your opponents to lock in $61 in stats for…$61. Uh-oh…you just got killed in the value game. Even with a roster of cheap freezes and tremendous value, you allowed your opponents to swoop in and close the distance significantly between your roster and theirs.

Let me use another extreme example. Let us assume I have Freddie Freeman with a raw bid of $23 and Michael Morse with a raw bid of $24. Chop $5 each off of those guys: do you want Freeman/Morse at $37 combined, or Votto at $53? I know my answer.

Why did I use these two particular examples? Simply put, these types of bargains are scarier than the end-game bargains. You cannot win a league solely by assembling a team of $1 players who earn $6. You can, however, win a league with a solid freeze list combined with top tier players at less than inflation par, assuming those players are not injured and/or do not pull an Adam Dunn.

Ultimately, the point is this: you cannot violate the simple value tenet of the auction. Each $1 of overpay equals a $1 of bargain at some point later in the auction. Give Joey his extra dollar or two, but let your opponents make the mistake of overpaying based on perceived position scarcity.

Individual players leaving or entering the player pool have a very small impact from season to season. Park factors have more of an impact, though the impact on the players who play in that venue is more significant than the impact on those who visit.